226 THE PRINCIPLES OF SCIENCE. 



event itself there can be no such uncertainty ; the steam- 

 vessel either has sunk or has not sunk, and no subsequent 

 discussion of the probable nature of the event can alter 

 the fact. Yet the probability of the event will really 

 vary from day to day, and from mind to mind, according 

 as the slightest information is gained regarding the vessels 

 met at sea, the weather prevailing there, the signs of 

 wreck picked up, or the previous condition of the vessel. 

 Probability thus belongs to our mental condition, to the 

 light in which we regard events, the occurrence or non- 

 occurrence of which is certain in themselves. Many 

 writers accordingly have asserted that probability is con- 

 cerned with degree or quantity of belief. De Morgan 

 says, b ' By degree of probability we really mean or ought 

 to mean degree of belief/ The late Professor Donkin 

 expressed the meaning of probability as 'quantity of 

 belief;' but I have never felt satisfied with such a defini- 

 tion of probability. The nature of belief is not more 

 clear to my mind than the notion it is used to define. 

 But an all-sufficient objection is, that the theory does not 

 measure what the belief is, but what it ought to be. Few ' 

 minds think in close accordance with the theory, and 

 there are many cases of evidence in which the belief 

 existing is habitually different from what it ought to be. 

 Even if the state of belief in any mind could be measured 

 and expressed in figures, the results would be worthless. 

 The very value of the theory consists in correcting and 

 guiding our belief, and rendering our states of mind and 

 consequent actions harmonious with our knowledge of 

 exterior conditions. 



This objection has been clearly perceived by some of 



those who still used quantity of belief as a definition of 



probability. Thus De Morgan adds ' Belief is but another 



name for imperfect knowledge/ Professor Donkin has 



b 'Formal Logic,' p. 172. 



